| Summary: | We study the dynamics of a spin-1/2 XXZ chain which is initially prepared in
a domain-wall state. We compare the results of time-dependent Density Matrix
Renormalization Group simulations with those of an effective description in
terms of a classical anisotropic Landau-Lifshitz (LL) equation. Numerous
quantities are analyzed: magnetization (x, y and z components), energy density,
energy current, but also some spin-spin correlation functions or entanglement
entropy in the quantum chain. Without any adjustable parameter a quantitative
agreement is observed between the quantum and the LL problems in the long time
limit, when the models are close to the isotropic point. This is explained as a
consequence of energy conservation. At the isotropic point the mapping between
the LL equation and the nonlinear Schr\"odinger equation is used to construct a
variational solution capturing several aspects of the problem.
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